Of the wide variety of catheters used in the treatment and diagnosis of the human body, many require considerable manipulation and steering in order that the distal end of the catheter can reach the treatment site within the patient's body and perform its intended function. A few examples of such catheters include dilating catheters, electroprobes, angiographic catheters and flow directed catheters. Typically such catheters are provided with a curved distal end and have a shaft that is sufficiently torsionally rigid so that the distal end of the catheter can be caused to rotate by the physician rotating the catheter at its proximal end. In order to achieve such torsional rigidity, it often is the practice to build the tubular catheter in a plurality of sequential layers, one or more of which may be adapted to increase the torque transmission of the catheter from its proximal to its distal end. For example, in order to increase the torque transmission capability of a catheter it is common practice to incorporate a tubular braid of strong material such as stainless steel or a high strength polymer into the wall of the catheter, as one of its layers. Additionally, the configuration of the layers often is varied so as to vary the stiffness of the catheter along its length, particularly to make the catheter more flexible toward its distal end. Among the disadvantages of the layer by layer construction and of incorporating the braided tube into the wall of the catheter is that they are time consuming, labor intensive and expensive procedures. It would be desirable, therefore, to provide a less complex and less expensive construction for such catheters and it is among the principal objects of the present invention to provide such a construction.